Investigation Of Topological Properties Of Non-hermitian Acoustic Crystals With Coupled Resonators Chains

With the development of science and technology,the acoustic properties of the acoustic materials have already can't meet our needs in terms of sound field control increasingly complex,it is because of natural materials can control the sound wave frequency range is limited,acoustic crystal is a kind of artificial periodic composite materials,its abundant acoustic field dispersion relations caused more and more attention.Acoustic waves are not allowed to propagate in the frequency range of acoustic band gap,sound insulation materials can be designed by using the properties of band gap.When defects are introduced into acoustic crystals,the periodicity of the structure is destroyed,and the defect states appear,which can be used to design sound energy collection or sound waveguide.Acoustic crystals designed according to actual needs can show some unique properties that cannot be realized by natural materials.In the early stage,acoustic crystals were mainly studied in band gap and defect states.In recent years,people began to study the topological properties of acoustic crystals,and found that similar to the valley Hall effect and spin quantum Hall effect in quantum systems,topological insulators and high-order topological insulators can be realized in acoustic crystals,making them a hot topic in the forefront of scientific research.Non-hermitian physics produces many interesting phenomena in classical wave systems and extends topological phases beyond the Hermitian system.Recently,non-Hermitian topological acoustic crystal systems derived from Hermitian components have attracted people's attention,but the physical mechanism of topological phase transition induced purely by non-Hermitian components remains unclear and needs further study.In this thesis,on the basis of predecessors,the topological properties of one-dimensional non-Hermitian acoustic crystals are deeply studied as follows:Firstly,we introduce the concepts of acoustic crystals and non-Hermitian topology respectively,and briefly summarize their research background and development status.Secondly,the basic theories of non-Hermitian topological properties of acoustic crystals are introduced,and the topological invariant and its calculation methods are also introduced.Thirdly,we propose a loss adjustable acoustic crystal model,which is composed of a one-dimensional coupled acoustic resonators chain,and each unit cell contains three or six resonators.The topological properties of the crystal are verified by calculating the defined topological invariant,and the the edge states of the acoustic crystal are observed experimentally.By studying the topological states when the number of resonators in the unit cell is odd or even,it is found that the position of the loss cavity affects the topological phase transition in acoustic crystals,which determines whether the band gap is trivial or not.Fourthly,the robustness of the model is verified by introducing defects.By changing the size and location of defects and the size of additional loss in one-dimensional finite resonators chains,the topological properties of the acoustic crystals designed by us are proved to be very robust.Finally,by introducing additional losses into tubes,the topological properties of the structure are also obtained.